Found with PFGW Version 3.4.8

45^12999-44 is 2-PRP! (12.8782s+0.0053s)
45^12999-44 is 3-PRP! (15.6962s+0.0055s)
45^12999-44 is 5-PRP! (20.5117s+0.0063s)
45^12999-44 is 7-PRP! (25.5696s+0.0076s)
45^12999-44 is 11-PRP! (29.0102s+0.0070s)

Primality testing 45^12999-44 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 10+sqrt(29)
Calling N-1 BLS with factored part 0.09% and helper 0.02% (0.30% proof)
45^12999-44 is Fermat and Lucas PRP! (235.2498s+0.0188s)

To be completed...